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x/6x-36-8=1/x-6
We move all terms to the left:
x/6x-36-8-(1/x-6)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: x-6)!=0We add all the numbers together, and all the variables
x∈R
x/6x-(1/x-6)-44=0
We get rid of parentheses
x/6x-1/x+6-44=0
We calculate fractions
x^2/6x^2+(-6x)/6x^2+6-44=0
We add all the numbers together, and all the variables
x^2/6x^2+(-6x)/6x^2-38=0
We multiply all the terms by the denominator
x^2+(-6x)-38*6x^2=0
Wy multiply elements
x^2-228x^2+(-6x)=0
We get rid of parentheses
x^2-228x^2-6x=0
We add all the numbers together, and all the variables
-227x^2-6x=0
a = -227; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-227)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-227}=\frac{0}{-454} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-227}=\frac{12}{-454} =-6/227 $
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